The face is the most important part of the human body for interpersonal communication, emotional expression, and most other forms of social interaction. The face is also the primary feature of the body by which people recognize one another. Even newborn infants have a natural ability to recognize familiar faces.
Throughout human history, societies have placed great emphasis and value on facial attractiveness. The significance of the aesthetics of the face is demonstrated by the thousands of works of art and sculpture dedicated to portraying attractive facial features. Modern research studies suggest that human beings have a natural tendency to prefer facial configurations that are aesthetically pleasing. Studies have shown that persons whose faces are attractive are more likely to be perceived as personable, intelligent, and are generally perceived as possessing a variety of positive attributes. Sociological researchers have chronicled many of the benefits enjoyed by those who are fortunate to be born with a configuration of facial features that is aesthetically pleasing. The benefits of having an attractive face have been shown to begin very early in life and to continue throughout the formative years and well into adulthood. It has been documented that parents tend to give more attention and care to babies with more attractive faces. Studies also reveal that teachers perceive attractive children as more intelligent and popular than their less attractive peers. In comparisons of facial attractiveness, better looking high school females were found to be enjoying a higher socioeconomic status 15 years later compared to their other classmates. Even in the military, when a class of West Point cadets were rated for attractiveness, and later compared with their rank achieved after graduation, the more attractive cadets tended to achieve a higher military rank than the less attractive cadets.
Recent sociological studies also suggest that the tendency of humans to prefer an attractive face is not learned from society or from constant exposure to the popular culture. Strong evidence suggests that perceptions of attractiveness or beauty are generally similar in persons in different nations and even in diverse cultures.
While it is oft said that "beauty is in the eye of the beholder," researchers have also discovered that perceptions of beauty vary little from culture to culture, and that perceptions of beauty do not vary substantially from person to person. When asked to rank photographs of 20 young women in the order of attractiveness, responses from over 100,000 Americans showed substantial agreement as to which photographs featured the most attractive faces. Furthermore, recent research has revealed that these perceptions begin shortly after birth. Researchers have discovered that even newly born infants show a positive reaction to photographs of attractive faces.
Unfortunately, those born with facial deformities are likely to suffer greatly from social prejudices. Throughout history, ridicule, ostracization, and even death have been inflicted on people who suffer from facial deformities.
Modern medicine and surgical techniques offer hope to those born with facial deformities or those whose faces are deformed from accident or disease. Today, surgeons can use X-ray models, synthetic implants and a variety of other techniques to improve facial appearance. However, although modern medicine offers improved techniques and materials, neither artists, surgeons, nor sociologists are presently able to understand why certain faces are perceived as attractive nor are those skilled in the art able to offer a technique to describe the physical parameters that, when viewed together as a human face, cause a face to be perceived as attractive.
Many attempts throughout history have been made to develop parameters to quantify idealized facial proportions and, in essence, to quantify human faces. Attempts to quantify human faces initially stemmed from the Greek philosophy that all beauty and aesthetics are based on mathematics. The Greeks proposed that all beauty could be quantitatively determined and analyzed, and that the essence of beauty in all things was mathematical. The Greeks showed great interest in a mathematical relationship called the "Golden Proportion" that is discussed in detail below. Following the Renaissance, the study of facial beauty, particularly in art, led to multiple attempts, most notably by Leonardo Da Vinci and Albrecht Durer, to quantify facial proportions and to establish a "norm" from which all faces could be analyzed.
In the last few centuries, the attempts to quantify facial proportions involved measuring distances of and between the facial features of persons considered normal or attractive by the individual performing the study. Significant studies with large numbers of subjects were not conducted until the twentieth century. In the last one hundred years, the studies were conducted primarily by plastic surgeons and orthodontists who were continually studying faces and attempting to quantify selected facial dimensions and proportions. Although the medical and dental literature is replete with studies of the face, there are certain inherent weaknesses in the studies.
Dentists, particularly orthodontists, are naturally interested in function and, rather than studying attractive faces and soft tissue parameters, dental studies tend to focus on faces having normal function and only then studying those faces for soft tissue parameters. Thus, the studies do not disclose detailed parameters for attractive faces, rather the studies tend to depict functional parameters or soft tissue aesthetic parameters which are common to people with "normal function" who may or may not be attractive.
Plastic surgeons have been interested primarily in soft tissue drape and focused their attention on measuring the parameters for ideal soft tissue drape configurations. The weakness of the medical literature is the tendency to study isolated facial soft-tissue topography as opposed to the entire face as a unit. Studies of the nasal angle, nasal frontal angle, nasal tip projection, etc., are helpful only in analyzing individual parts of the face and give little or no information regarding an ideal or aesthetically pleasing relationship of those features to the rest of the face.
The general weakness in this literature is a tendency to borrow parameters and canons for soft tissue aesthetics from the artists of the classical and Renaissance periods. Much of the contemporary literature in this area merely restates these classical canons adhered to by early artists.
Although techniques for orthodontics as well as oral surgery and plastic surgery have become extremely sophisticated. Whether one is controlling development of the facial bones or teeth through orthodontics, restructuring facial bones through oral or reconstructive surgery, or reconfiguring facial soft tissue through plastic surgery, the technical expertise to perform these procedures has advanced far beyond the ability to comprehensively diagnose variations from an ideal facial form because an apparatus or technique to analyze the face as a whole and to provide a guide towards achieving an overall attractive appearance does not presently exist. Therefore, the improvements in technical skills in medicine and dentistry in the twentieth century, particularly in orthodontics, oral surgery, and plastic surgery, heightens the need to develop unifying parameters for an ideal facial form.
Early Greek mathematicians discovered that it is possible to describe a mathematical relationship between two linear distances as follows: ##EQU1## such that the distance from P to Q when compared to the distance from Q to R, has the same ratio as the distance from Q to R compared to the distance from P to R. This relationship applies only when the ratio of the distance between Q and R and the distance between P and Q is 1.618 18 or approximately 89/55. Greek mathematicians recognized the unique properties of a mathematical proportion where the ratio between the greater proportion and smaller part is equal to the ratio between the whole and the greater part. This proportion, typically indicated with the Greek letter .PHI., has been called the "Golden Proportion" or the "Golden Section" and has long been used by artists, architects, and other scholars to create aesthetically pleasing works of art and structures. Architects studying the Parthenon built on the Acropolis in Athens, Greece in the Fifth Century B.C. have noted that the Golden Proportion is reflected in the architectural design of the frontal view of the Parthenon.
As used here, the greek letter Phi (.PHI.) represents the "golden proportion" or its numerical value (.apprxeq.89/55). Using phi, identical sets of numbers can be generated through both geometric and arithmetic progressions. For example, setting .PHI.=1,618, a geometric progression can be defined as follows:
1.000.times..PHI.=1.618 PA1 1.618.times..PHI.=2,618 PA1 2.618.times..PHI.=4.236 PA1 4.236.times..PHI.=6.854 PA1 6.854.times..PHI.=11.090 PA1 1,000+.PHI.=2.618 PA1 .PHI.+2.618=4,236 PA1 2.618+4,236=6.854 PA1 4,236+6.854=11.090 PA1 (1) analyze the aesthetics of a face with respect to the overlay systems to aid in applying cosmetics or planning surgical corrections or other treatments to correct variations from a desired appearance (e.g., augmentation, reduction or repositioning of facial parts or components); PA1 (2) quantify facial proportions relative to the overlay systems or pentagon complexes; and PA1 (3) mathematically quantify individual facial proportions, for example, for security or identification purposes. PA1 (1) a primary pentagon complex which forms a basic framework for the overlay system and from which specific lines, line segments, and points have been selected to construct the component lines and points of the overlay system; and PA1 (2) various secondary pentagon complexes, the sizes of which are mathematically related to the primary pentagon complex and from which specific lines, line segments, and points have been selected to construct the component lines and points of the overlay system. PA1 (1) A lateral view image of the person's face is recorded (e.g., via photograph, computer, etc.) ensuring that the expression of the face is properly posed and that the head is properly positioned. PA1 (2) Anthropometric points are established on the facial image. PA1 (3) An overlay system containing a lateral view in repose (FIG. 1) is placed upon the image and certain anthropomorphic points of the overlay system are aligned with those marked on the facial image. PA1 (4) The lateral overlay system is sized, oriented, and adjusted to the facial image to enable a comparison between the overlay system and the image. PA1 (5) The facial image is compared to the overlay system and the variations noted or measured. PA1 1) Pupil Point (PU)--the center of the pupil 1 seen in a frontal view and the most anterior point of the pupil 1 seen in a profile view. PA1 2) Tragion (T)--the notch 2 on the upper margin of the tragus 25. PA1 3) Cheilion (CH)--the most lateral extent 3 of the outline of the lips. PA1 4) Porion (POR)--the highest point 4 on the upper margin at the cutaneous auditory meatus. PA1 5) Otobasion Inferius (OBI)--the point 5 of attachment of the ear lobe to the cheek. PA1 6) Alare Posterior (AP)--the most posterior point 6 of the soft tissue outline of the lateral cartilaginous wall of the naris. PA1 7) Glabella (GS)--the most anterior point 7 on the soft-tissue forehead. PA1 8) Nasion (NS)--the most concave point 8 of the soft-tissue outline of the bridge of the nose. PA1 9) Trichion (TRU)--the point 9 on the hairline in the midline of the forehead. In early childhood, identification of this landmark may be difficult because of an irregular or indistinguishable hairline. It cannot be determined on a balding head. PA1 10) Pronasale (PRN)--the most anterior point 10 of the nose. PA1 11) Menton (MES)--the most inferior point 11 of the soft-tissue outline of the chin. PA1 12) Pogonion (PGS)--the most anterior point 12 on the convexity of the soft-tissue chin. PA1 13) Inferior Palpebrion (IPR)--the most inferior point 13 of the inferior palpebral line on the right lower eyelid. PA1 14) Subtragion (SBT)--the point 14 where the tragus joins the intertragal notch. PA1 15) Subnasale (SBN)--the point 15 at which the columella merges with the upper cutaneous lip. PA1 16) Vermilion Superius (VS)--the point 16 at the intersection between the vermilion border of the upper lip and the cutaneous portion of the upper lip. PA1 17) Labrale Superius (LS)--the most anterior point 17 on the convexity of the upper lip. PA1 18) Upper Stomion (UST)--the most inferior point 18 of the anterior portion of the upper lip. PA1 19) Lower Stomion (LST)--the most superior point 19 on the anterior portion of the lower lip. PA1 20) Labrale Inferius (LI)--the most anterior point 20 on the convexity of the lower lip. PA1 21) Vermilion Inferius (VI)--the point 21 of intersection between the vermilion border of the lower lip and the cutaneous portion of the lower lip. PA1 22) Gnathion (GNS)--the most everted point 22 of the soft-tissue chin between the Pogonion 12 and the Menton 11. PA1 23) Gonion (GN)--the most posterior point 23 of the lower mandible. PA1 24) Malar Point (MLR)--the most everted point 24 on the convexity of the cheek. PA1 25) Tragus (TRG)--the soft-tissue lobe 25 between the tragion 2 and the subtragion 14.
the corresponding arithmetic progression is:
Thus, .PHI. is unique. The same set of numbers is generated both geometrically and arithmetically and any product in the geometric progression can be determined by adding the two preceding products in the sequence.
These unusual properties of phi are well known. In addition, much has been written about the occurrence of the phi proportion in nature. A number of examples of the Golden Proportion can be found in animal and plant life and the importance of the natural symmetry of the Golden Proportion has been studied in the context of biological growth mechanisms. For example, the Golden Proportion is reflected in the structure of a number of flowers and when applied mathematically to construct a spiral shape, describes the appearance of certain shell types. The Golden Proportion was applied to human aesthetics as early as the ancient Greeks who noted that the distances from the top of the head to the navel and from the navel to the feet were related to each other, and to the total height of the body, by the Golden Proportion .PHI..
The Golden Proportion has been recognized as describing an aesthetically pleasing relationship between the sizes of the frontal upper teeth when viewed from the front and has been applied by a number of scholars in making linear measurements to analyze dental aesthetics. Beyond application to the teeth, a number of researchers have noted the appearance of the Golden Proportion in measuring the linear distances between certain points on the face. For example, in the attractive face the width of the mouth in repose is roughly 1.618 multiplied by the width of the nose. In the 1946 book The Geometry of Art and Life, Professor M. Ghyka undertakes a detailed and comprehensive analysis of the Golden Proportion (.PHI.) and its application to biological systems. Professor Ghyka notes that the .PHI. ratio, in an "average or ideal" face, describes the vertical linear distance of the face and the distance from the line of the eye brows to the lower chin. The .PHI. ratio also is noted to describe the linear vertical distance from the lower part of the nose to the lower tip of the chin and the lower tip of the chin to the meeting line of the lips. Ghyka applied rectangles containing line segments corresponding to the Golden Proportion to the frontal view of the face of an Olympic athlete. Furthermore, a practical application of the principles set forth by Ghyka to plastic surgery is discussed in "The Golden Proportion and Beauty" a medical journal article published in 1964. Doctors used the rectangular relationships noted by Ghyka to repair a severe facial deformity in a patient resulting from untreated facial fractures suffered in childhood.